The Chinese government reacted to the Dalai Lama's visit to the White House last Saturday with anger. A spokesman lashed out at the exiled Tibetan leader for his supposedly "anti-China splittist activities." Barack Obama deserves credit for continuing the tradition of U.S. presidents meeting with the Dalai Lama. But maintaining American policy on Tibet will also require Mr. Obama to acknowledge new realities in the Tibetan exile community.

Preparing for the day when the Chinese government stage manages the selection of his successor, the Dalai Lama in May turned over the secular leadership of his people to an elected government. Lobsang Sangay won election in April as kalon tripa, or chief minister, and is due to take office next month in Dharamsala, India, the seat of the exile government.

Washington has long maintained contact with the Dalai Lama to help refugees and preserve Tibetan culture and religion. The change in the Tibetan government presents a challenge to President Obama to bring American policy toward Tibet in line with the support for democracy and self-determination that he has often expressed. Speaking up for the human rights of Tibetans will require a new protocol of unofficial contacts with the Tibetan movement, even as the U.S. continues to recognize the Chinese government's sovereignty over Tibet.

Beijing will no doubt react harshly to this move, just as it did to Mr. Sangay's election. A spokesman for the United Front Work Department, the Communist Party unit that is responsible for "dialogue" with the Dalai Lama, denounced the India-based Central Tibetan Administration as a "separatist political clique that betrays the motherland, with no legitimacy at all."

At present Washington essentially takes China's position, albeit in kinder terms. The U.S. does not recognize Tibetan sovereignty and accepts Beijing's assertion of control. Elected officials of the CTA, like Mr. Sangay, are not welcome at the State Department and the White House.

America's interests regarding Tibet are strategic as well as moral. China intends to choose the next Dalai Lama and has promulgated "guidelines on reincarnation" that emphasize patriotism and love of the motherland. The Dalai Lama himself has said that his reincarnation will be found in a free country, following the principle that a reincarnation continues the work of his predecessor. If the succession dispute is allowed to come to loggerheads, Beijing may respond, according to scholar Daniel Twining, "by deploying the People's Liberation Army to occupy contested territory along the Sino-Indian border, as occurred in 1962, creating a risk of military conflict between the now nuclear-armed Asian giants."

Washington and other Western countries should engage in pre-emptive moves of their own to recognize the changes that the Tibetan diaspora has effected by enhancing ties with the Tibetan exile government, which will take on more importance as the sole repository of Tibetan political authority. The West should also embrace the Dalai Lama's process for identifying his successor. A firm position on both could help stop Beijing from escalating pressure on Washington's relations with Tibetans in exile.

Taiwan provides a model for how the U.S. could maintain ties with the exiled Tibetan government. The U.S. has a system of unofficial diplomatic relations with Taipei despite Beijing's claim that Taiwan is part of China. Over time as Taiwan democratized, U.S. policy incorporated support for the island's self-determination, stipulating that any resolution of its dispute with China should be made "with the assent of the people of Taiwan."

Although there are obvious differences between the two cases—Taiwan enjoys de facto independence and Tibet is occupied—the Tibetan government-in-exile has achieved democracy and legitimacy as the true representatives of the Tibetan people. The kalon tripa gaining greater international recognition could ultimately put pressure on Beijing to moderate its policies within Tibet itself.

As with Taiwan, a revised U.S. policy toward Tibet does not need to settle the issue of sovereignty. The Dalai Lama no longer seeks independence—merely autonomy under Chinese rule. Even if Tibet had always been part of a "multinational state," as Chinese propaganda claims, American support for democracy there as well as in China would advance universal values and American interests.

"We are the nations most willing to stand up for the values of tolerance and self-determination that lead to peace and dignity" President Obama told British members of parliament in May. Indeed, America once placed great importance on Tibet's self-determination. In 1961, then President John F. Kennedy expressed Americans' hopes that "Tibet will one day be governed in accordance with the manifest wishes of the Tibetan people." The consolidation of Tibet's democracy-in-exile under Mr. Sangay presents an opportunity for the U.S. to make those aspirations part of its policy.

Ms. Bork is director of democracy and human rights at the Foreign Policy Initiative.